LMFDB - Embedded newform 943.1.n.b.689.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [943,1,Mod(367,943)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(943, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 3]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("943.367");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 943 = 23 \cdot 41 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	943.n (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.470618306913$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{60}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{60} - \cdots)$

Embedding invariants

Embedding label			689.1
Root			$-0.743145 + 0.669131i$ of defining polynomial
Character	$\chi$	$=$	943.689
Dual form			943.1.n.b.620.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07394 + 1.47815i) q^{2} +(-1.41228 + 1.41228i) q^{3} +(-0.722562 - 2.22382i) q^{4} +(-0.570857 - 3.60425i) q^{6} +(2.32545 + 0.755585i) q^{8} -2.98904i q^{9} +O(q^{10})$	\(q+(-1.07394 + 1.47815i) q^{2} +(-1.41228 + 1.41228i) q^{3} +(-0.722562 - 2.22382i) q^{4} +(-0.570857 - 3.60425i) q^{6} +(2.32545 + 0.755585i) q^{8} -2.98904i q^{9} +(4.16110 + 2.12019i) q^{12} +(1.65669 - 0.262394i) q^{13} +(-1.72256 + 1.25151i) q^{16} +(4.41825 + 3.21005i) q^{18} +(-0.809017 - 0.587785i) q^{23} +(-4.35127 + 2.21708i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-1.39132 + 2.73063i) q^{26} +(2.80908 + 2.80908i) q^{27} +(-0.0932634 - 0.0475201i) q^{29} +(0.459289 - 1.41355i) q^{31} -1.44512i q^{32} +(-6.64709 + 2.15977i) q^{36} +(-1.96913 + 2.71028i) q^{39} +(0.913545 - 0.406737i) q^{41} +(1.73767 - 0.564602i) q^{46} +(-0.196895 - 1.24314i) q^{47} +(0.665249 - 4.20022i) q^{48} +(-0.951057 - 0.309017i) q^{49} +1.82709i q^{50} +(-1.78058 - 3.49458i) q^{52} +(-7.16900 + 1.13546i) q^{54} +(0.170401 - 0.0868235i) q^{58} +(-0.500000 - 0.363271i) q^{59} +(1.59618 + 2.19696i) q^{62} +(0.413545 + 0.300458i) q^{64} +(1.97267 - 0.312440i) q^{69} +(0.847673 + 1.66365i) q^{71} +(2.25848 - 6.95088i) q^{72} +0.415823i q^{73} +(-0.312440 + 1.97267i) q^{75} +(-1.89147 - 5.82133i) q^{78} -4.94534 q^{81} +(-0.379874 + 1.78716i) q^{82} +(0.198825 - 0.0646021i) q^{87} +(-0.722562 + 2.22382i) q^{92} +(1.34767 + 2.64496i) q^{93} +(2.04900 + 1.04402i) q^{94} +(2.04091 + 2.04091i) q^{96} +(1.47815 - 1.07394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6	$ 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6} + 2 q^{13} - 6 q^{16} + 6 q^{18} - 4 q^{23} - 22 q^{24} + 4 q^{25} + 12 q^{26} + 6 q^{27} - 8 q^{29} - 10 q^{36} + 2 q^{41} + 2 q^{47} - 18 q^{48} - 6 q^{54} + 2 q^{58} - 8 q^{59} - 10 q^{62} - 6 q^{64} - 2 q^{69} - 2 q^{71} + 16 q^{72} + 2 q^{75} - 2 q^{78} - 12 q^{81} + 10 q^{92} + 6 q^{93} + 18 q^{94} - 10 q^{96} + 6 q^{98}+O(q^{100}) $ 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6 + 2 * q^13 - 6 * q^16 + 6 * q^18 - 4 * q^23 - 22 * q^24 + 4 * q^25 + 12 * q^26 + 6 * q^27 - 8 * q^29 - 10 * q^36 + 2 * q^41 + 2 * q^47 - 18 * q^48 - 6 * q^54 + 2 * q^58 - 8 * q^59 - 10 * q^62 - 6 * q^64 - 2 * q^69 - 2 * q^71 + 16 * q^72 + 2 * q^75 - 2 * q^78 - 12 * q^81 + 10 * q^92 + 6 * q^93 + 18 * q^94 - 10 * q^96 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/943\mathbb{Z}\right)^\times$.

$n$	$47$	$534$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.07394	+	1.47815i	−1.07394	+	1.47815i	−0.207912	+	0.978148i	$0.566667\pi$
$2$	−1.07394	+	1.47815i	−1.07394	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−1.41228	+	1.41228i	−1.41228	+	1.41228i	−0.669131	+	0.743145i	$0.733333\pi$
$3$	−1.41228	+	1.41228i	−1.41228	+	1.41228i	−0.743145	+	0.669131i	$0.766667\pi$
$4$	−0.722562	−	2.22382i	−0.722562	−	2.22382i
$5$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$5$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$6$	−0.570857	−	3.60425i	−0.570857	−	3.60425i
$7$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$7$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$8$	2.32545	+	0.755585i	2.32545	+	0.755585i
$9$		−	2.98904i		−	2.98904i
$10$		0			0
$11$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$11$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$12$	4.16110	+	2.12019i	4.16110	+	2.12019i
$13$	1.65669	−	0.262394i	1.65669	−	0.262394i	0.743145	−	0.669131i	$-0.233333\pi$
$13$	1.65669	−	0.262394i	1.65669	−	0.262394i	0.913545	+	0.406737i	$0.133333\pi$
$14$		0			0
$15$		0			0
$16$	−1.72256	+	1.25151i	−1.72256	+	1.25151i
$17$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$17$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$18$	4.41825	+	3.21005i	4.41825	+	3.21005i
$19$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$19$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$23$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$24$	−4.35127	+	2.21708i	−4.35127	+	2.21708i
$25$	0.809017	−	0.587785i	0.809017	−	0.587785i
$26$	−1.39132	+	2.73063i	−1.39132	+	2.73063i
$27$	2.80908	+	2.80908i	2.80908	+	2.80908i
$28$		0			0
$29$	−0.0932634	−	0.0475201i	−0.0932634	−	0.0475201i	0.406737	−	0.913545i	$-0.366667\pi$
$29$	−0.0932634	−	0.0475201i	−0.0932634	−	0.0475201i	−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$	0.459289	−	1.41355i	0.459289	−	1.41355i	−0.406737	−	0.913545i	$-0.633333\pi$
$31$	0.459289	−	1.41355i	0.459289	−	1.41355i	0.866025	−	0.500000i	$-0.166667\pi$
$32$		−	1.44512i		−	1.44512i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−6.64709	+	2.15977i	−6.64709	+	2.15977i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$		0			0
$39$	−1.96913	+	2.71028i	−1.96913	+	2.71028i
$40$		0			0
$41$	0.913545	−	0.406737i	0.913545	−	0.406737i
$41$	0.913545	−	0.406737i	0.913545	−	0.406737i
$42$		0			0
$43$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$43$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$44$		0			0
$45$		0			0
$46$	1.73767	−	0.564602i	1.73767	−	0.564602i
$47$	−0.196895	−	1.24314i	−0.196895	−	1.24314i	−0.866025	−	0.500000i	$-0.833333\pi$
$47$	−0.196895	−	1.24314i	−0.196895	−	1.24314i	0.669131	−	0.743145i	$-0.266667\pi$
$48$	0.665249	−	4.20022i	0.665249	−	4.20022i
$49$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$50$			1.82709i			1.82709i
$51$		0			0
$52$	−1.78058	−	3.49458i	−1.78058	−	3.49458i
$53$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$53$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$54$	−7.16900	+	1.13546i	−7.16900	+	1.13546i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.170401	−	0.0868235i	0.170401	−	0.0868235i
$59$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$59$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$61$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$62$	1.59618	+	2.19696i	1.59618	+	2.19696i
$63$		0			0
$64$	0.413545	+	0.300458i	0.413545	+	0.300458i
$65$		0			0
$66$		0			0
$67$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$67$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$68$		0			0
$69$	1.97267	−	0.312440i	1.97267	−	0.312440i
$70$		0			0
$71$	0.847673	+	1.66365i	0.847673	+	1.66365i	0.743145	+	0.669131i	$0.233333\pi$
$71$	0.847673	+	1.66365i	0.847673	+	1.66365i	0.104528	+	0.994522i	$0.466667\pi$
$72$	2.25848	−	6.95088i	2.25848	−	6.95088i
$73$			0.415823i			0.415823i	0.978148	+	0.207912i	$0.0666667\pi$
$73$			0.415823i			0.415823i	−0.978148	+	0.207912i	$0.933333\pi$
$74$		0			0
$75$	−0.312440	+	1.97267i	−0.312440	+	1.97267i
$76$		0			0
$77$		0			0
$78$	−1.89147	−	5.82133i	−1.89147	−	5.82133i
$79$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$79$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$80$		0			0
$81$	−4.94534			−4.94534
$82$	−0.379874	+	1.78716i	−0.379874	+	1.78716i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.198825	−	0.0646021i	0.198825	−	0.0646021i
$88$		0			0
$89$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$89$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$90$		0			0
$91$		0			0
$92$	−0.722562	+	2.22382i	−0.722562	+	2.22382i
$93$	1.34767	+	2.64496i	1.34767	+	2.64496i
$94$	2.04900	+	1.04402i	2.04900	+	1.04402i
$95$		0			0
$96$	2.04091	+	2.04091i	2.04091	+	2.04091i
$97$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$97$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$98$	1.47815	−	1.07394i	1.47815	−	1.07394i
$99$		0			0
$100$	−1.89169	−	1.37440i	−1.89169	−	1.37440i
$101$	0.896802	+	0.142040i	0.896802	+	0.142040i	0.587785	−	0.809017i	$-0.300000\pi$
$101$	0.896802	+	0.142040i	0.896802	+	0.142040i	0.309017	+	0.951057i	$0.400000\pi$
$102$		0			0
$103$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$103$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$104$	4.05081	+	0.641586i	4.05081	+	0.641586i
$105$		0			0
$106$		0			0
$107$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$107$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$108$	4.21715	−	8.27661i	4.21715	−	8.27661i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$113$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$114$		0			0
$115$		0			0
$116$	−0.0382874	+	0.241737i	−0.0382874	+	0.241737i
$117$	−0.784307	−	4.95192i	−0.784307	−	4.95192i
$118$	1.07394	−	0.348943i	1.07394	−	0.348943i
$119$		0			0
$120$		0			0
$121$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$122$		0			0
$123$	−0.715754	+	1.86460i	−0.715754	+	1.86460i
$124$	−3.47533			−3.47533
$125$		0			0
$126$		0			0
$127$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$127$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$128$	0.486152	−	0.157960i	0.486152	−	0.157960i
$129$		0			0
$130$		0			0
$131$	1.86055	+	0.604528i	1.86055	+	0.604528i	0.994522	+	0.104528i	$0.0333333\pi$
$131$	1.86055	+	0.604528i	1.86055	+	0.604528i	0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	−1.65669	+	3.25144i	−1.65669	+	3.25144i
$139$	0.658114	−	0.478148i	0.658114	−	0.478148i	−0.207912	−	0.978148i	$-0.566667\pi$
$139$	0.658114	−	0.478148i	0.658114	−	0.478148i	0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$	2.03373	+	1.47759i	2.03373	+	1.47759i
$142$	−3.36947	−	0.533672i	−3.36947	−	0.533672i
$143$		0			0
$144$	3.74083	+	5.14881i	3.74083	+	5.14881i
$145$		0			0
$146$	−0.614648	−	0.446568i	−0.614648	−	0.446568i
$147$	1.77957	−	0.906737i	1.77957	−	0.906737i
$148$		0			0
$149$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$149$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$150$	−2.58036	−	2.58036i	−2.58036	−	2.58036i
$151$	−1.07587	+	0.170401i	−1.07587	+	0.170401i	−0.669131	−	0.743145i	$-0.733333\pi$
$151$	−1.07587	+	0.170401i	−1.07587	+	0.170401i	−0.406737	+	0.913545i	$0.633333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	7.44998	+	2.42065i	7.44998	+	2.42065i
$157$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$157$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	5.31098	−	7.30994i	5.31098	−	7.30994i
$163$	0.415823			0.415823			0.207912	−	0.978148i	$-0.433333\pi$
$163$	0.415823			0.415823			0.207912	+	0.978148i	$0.433333\pi$
$164$	−1.56460	−	1.73767i	−1.56460	−	1.73767i
$165$		0			0
$166$		0			0
$167$	0.642040	−	0.642040i	0.642040	−	0.642040i	−0.309017	−	0.951057i	$-0.600000\pi$
$167$	0.642040	−	0.642040i	0.642040	−	0.642040i	0.951057	+	0.309017i	$0.100000\pi$
$168$		0			0
$169$	1.72472	−	0.560394i	1.72472	−	0.560394i
$170$		0			0
$171$		0			0
$172$		0			0
$173$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$173$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$174$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$175$		0			0
$176$		0			0
$177$	1.21918	−	0.193099i	1.21918	−	0.193099i
$178$		0			0
$179$	0.877042	−	1.72129i	0.877042	−	1.72129i	0.207912	−	0.978148i	$-0.433333\pi$
$179$	0.877042	−	1.72129i	0.877042	−	1.72129i	0.669131	−	0.743145i	$-0.266667\pi$
$180$		0			0
$181$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$181$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$182$		0			0
$183$		0			0
$184$	−1.43721	−	1.97815i	−1.43721	−	1.97815i
$185$		0			0
$186$	−5.35695	−	0.848458i	−5.35695	−	0.848458i
$187$		0			0
$188$	−2.62226	+	1.33611i	−2.62226	+	1.33611i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−1.00837	+	0.159710i	−1.00837	+	0.159710i
$193$	1.49452	+	0.761497i	1.49452	+	0.761497i	0.994522	−	0.104528i	$-0.0333333\pi$
$193$	1.49452	+	0.761497i	1.49452	+	0.761497i	0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$		0			0
$196$			2.33826i			2.33826i
$197$	−1.89169	−	0.614648i	−1.89169	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$197$	−1.89169	−	0.614648i	−1.89169	−	0.614648i	−0.913545	−	0.406737i	$-0.866667\pi$
$198$		0			0
$199$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$199$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$200$	2.32545	−	0.755585i	2.32545	−	0.755585i
$201$		0			0
$202$	−1.17306	+	1.17306i	−1.17306	+	1.17306i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.75692	+	2.41819i	−1.75692	+	2.41819i
$208$	−2.52536	+	2.52536i	−2.52536	+	2.52536i
$209$		0			0
$210$		0			0
$211$	−0.0489435	−	0.309017i	−0.0489435	−	0.309017i	0.951057	−	0.309017i	$-0.100000\pi$
$211$	−0.0489435	−	0.309017i	−0.0489435	−	0.309017i	−1.00000			$\pi$
$212$		0			0
$213$	−3.54668	−	1.15239i	−3.54668	−	1.15239i
$214$		0			0
$215$		0			0
$216$	4.40988	+	8.65487i	4.40988	+	8.65487i
$217$		0			0
$218$		0			0
$219$	−0.587257	−	0.587257i	−0.587257	−	0.587257i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$223$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$224$		0			0
$225$	−1.75692	−	2.41819i	−1.75692	−	2.41819i
$226$		0			0
$227$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$227$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$228$		0			0
$229$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$229$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$230$		0			0
$231$		0			0
$232$	−0.180974	−	0.180974i	−0.180974	−	0.180974i
$233$	−1.90807	+	0.302208i	−1.90807	+	0.302208i	−0.994522	−	0.104528i	$-0.966667\pi$
$233$	−1.90807	+	0.302208i	−1.90807	+	0.302208i	−0.913545	+	0.406737i	$0.866667\pi$
$234$	8.16196	+	4.15873i	8.16196	+	4.15873i
$235$		0			0
$236$	−0.446568	+	1.37440i	−0.446568	+	1.37440i
$237$		0			0
$238$		0			0
$239$	0.0163743	−	0.103383i	0.0163743	−	0.103383i	−0.978148	−	0.207912i	$-0.933333\pi$
$239$	0.0163743	−	0.103383i	0.0163743	−	0.103383i	0.994522	+	0.104528i	$0.0333333\pi$
$240$		0			0
$241$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$241$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$242$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$243$	4.17510	−	4.17510i	4.17510	−	4.17510i
$244$		0			0
$245$		0			0
$246$	−1.98748	−	3.06045i	−1.98748	−	3.06045i
$247$		0			0
$248$	2.13611	−	2.94010i	2.13611	−	2.94010i
$249$		0			0
$250$		0			0
$251$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$251$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$252$		0			0
$253$		0			0
$254$	−1.73767	−	0.564602i	−1.73767	−	0.564602i
$255$		0			0
$256$	−0.446568	+	1.37440i	−0.446568	+	1.37440i
$257$	−0.494522	−	0.970554i	−0.494522	−	0.970554i	−0.994522	−	0.104528i	$-0.966667\pi$
$257$	−0.494522	−	0.970554i	−0.494522	−	0.970554i	0.500000	−	0.866025i	$-0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.142040	+	0.278768i	−0.142040	+	0.278768i
$262$	−2.89169	+	2.10094i	−2.89169	+	2.10094i
$263$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$263$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.336408	−	0.244415i	−0.336408	−	0.244415i	0.406737	−	0.913545i	$-0.366667\pi$
$269$	−0.336408	−	0.244415i	−0.336408	−	0.244415i	−0.743145	+	0.669131i	$0.766667\pi$
$270$		0			0
$271$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$271$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−2.12019	−	4.16110i	−2.12019	−	4.16110i
$277$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	0.406737	+	0.913545i	$0.366667\pi$
$277$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	−0.866025	+	0.500000i	$0.833333\pi$
$278$			1.48629i			1.48629i
$279$	−4.22515	−	1.37283i	−4.22515	−	1.37283i
$280$		0			0
$281$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$281$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$282$	−4.36820	+	1.41931i	−4.36820	+	1.41931i
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	3.08716	−	3.08716i	3.08716	−	3.08716i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.31954			−4.31954
$289$	0.587785	−	0.809017i	0.587785	−	0.809017i
$290$		0			0
$291$		0			0
$292$	0.924716	−	0.300458i	0.924716	−	0.300458i
$293$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$293$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$294$	−0.570857	+	3.60425i	−0.570857	+	3.60425i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.49452	−	0.761497i	−1.49452	−	0.761497i
$300$	4.61262	−	0.730567i	4.61262	−	0.730567i
$301$		0			0
$302$	0.903536	−	1.77329i	0.903536	−	1.77329i
$303$	−1.46713	+	1.06593i	−1.46713	+	1.06593i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.690983	+	0.951057i	0.690983	+	0.951057i	1.00000			$0$
$307$	0.690983	+	0.951057i	0.690983	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.638616	−	0.325391i	0.638616	−	0.325391i	−0.104528	−	0.994522i	$-0.533333\pi$
$311$	0.638616	−	0.325391i	0.638616	−	0.325391i	0.743145	+	0.669131i	$0.233333\pi$
$312$	−6.62696	+	4.81477i	−6.62696	+	4.81477i
$313$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$313$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.142040	−	0.278768i	−0.142040	−	0.278768i	0.809017	−	0.587785i	$-0.200000\pi$
$317$	−0.142040	−	0.278768i	−0.142040	−	0.278768i	−0.951057	+	0.309017i	$0.900000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	3.57332	+	10.9975i	3.57332	+	10.9975i
$325$	1.18606	−	1.18606i	1.18606	−	1.18606i
$326$	−0.446568	+	0.614648i	−0.446568	+	0.614648i
$327$		0			0
$328$	2.43173	−	0.255585i	2.43173	−	0.255585i
$329$		0			0
$330$		0			0
$331$	−1.09905	+	1.09905i	−1.09905	+	1.09905i	−0.104528	+	0.994522i	$0.533333\pi$
$331$	−1.09905	+	1.09905i	−1.09905	+	1.09905i	−0.994522	+	0.104528i	$0.966667\pi$
$332$		0			0
$333$		0			0
$334$	0.259519	+	1.63854i	0.259519	+	1.63854i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−1.02389	+	3.15121i	−1.02389	+	3.15121i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−2.39169	−	1.73767i	−2.39169	−	1.73767i
$347$	1.76007	+	0.278768i	1.76007	+	0.278768i	0.951057	−	0.309017i	$-0.100000\pi$
$347$	1.76007	+	0.278768i	1.76007	+	0.278768i	0.809017	+	0.587785i	$0.200000\pi$
$348$	−0.287327	−	0.395472i	−0.287327	−	0.395472i
$349$	−1.14988	−	1.58268i	−1.14988	−	1.58268i	−0.743145	−	0.669131i	$-0.766667\pi$
$349$	−1.14988	−	1.58268i	−1.14988	−	1.58268i	−0.406737	−	0.913545i	$-0.633333\pi$
$350$		0			0
$351$	5.39086	+	3.91669i	5.39086	+	3.91669i
$352$		0			0
$353$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	−0.866025	−	0.500000i	$-0.833333\pi$
$353$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	0.207912	+	0.978148i	$0.433333\pi$
$354$	−1.02389	+	2.00950i	−1.02389	+	2.00950i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.60244	+	3.14496i	1.60244	+	3.14496i
$359$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$359$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$360$		0			0
$361$	0.951057	+	0.309017i	0.951057	+	0.309017i
$362$		0			0
$363$	−0.312440	−	1.97267i	−0.312440	−	1.97267i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$367$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$368$	2.12920			2.12920
$369$	−1.21575	−	2.73063i	−1.21575	−	2.73063i
$370$		0			0
$371$		0			0
$372$	4.90813	−	4.90813i	4.90813	−	4.90813i
$373$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$373$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$374$		0			0
$375$		0			0
$376$	0.481432	−	3.03964i	0.481432	−	3.03964i
$377$	−0.166977	−	0.0542543i	−0.166977	−	0.0542543i
$378$		0			0
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$	−1.77957	−	0.906737i	−1.77957	−	0.906737i
$382$		0			0
$383$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$383$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$384$	−0.463497	+	0.909664i	−0.463497	+	0.909664i
$385$		0			0
$386$	−2.73063	+	1.39132i	−2.73063	+	1.39132i
$387$		0			0
$388$		0			0
$389$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$389$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$390$		0			0
$391$		0			0
$392$	−1.97815	−	1.43721i	−1.97815	−	1.43721i
$393$	−3.48137	+	1.77384i	−3.48137	+	1.77384i
$394$	2.94010	−	2.13611i	2.94010	−	2.13611i
$395$		0			0
$396$		0			0
$397$	1.90807	−	0.302208i	1.90807	−	0.302208i	0.913545	−	0.406737i	$-0.133333\pi$
$397$	1.90807	−	0.302208i	1.90807	−	0.302208i	0.994522	+	0.104528i	$0.0333333\pi$
$398$		0			0
$399$		0			0
$400$	−0.657960	+	2.02499i	−0.657960	+	2.02499i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	0.389993	−	2.46232i	0.389993	−	2.46232i
$404$	−0.332126	−	2.09696i	−0.332126	−	2.09696i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$409$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.68762	−	5.19396i	−1.68762	−	5.19396i
$415$		0			0
$416$	−0.379192	−	2.39412i	−0.379192	−	2.39412i
$417$	−0.254162	+	1.60471i	−0.254162	+	1.60471i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$421$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$422$	0.509335	+	0.259519i	0.509335	+	0.259519i
$423$	−3.71581	+	0.588527i	−3.71581	+	0.588527i
$424$		0			0
$425$		0			0
$426$	5.51231	−	4.00493i	5.51231	−	4.00493i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$	−8.35441	−	1.32321i	−8.35441	−	1.32321i
$433$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$433$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.49873	−	0.237376i	1.49873	−	0.237376i
$439$	0.638616	+	0.325391i	0.638616	+	0.325391i	0.743145	−	0.669131i	$-0.233333\pi$
$439$	0.638616	+	0.325391i	0.638616	+	0.325391i	−0.104528	+	0.994522i	$0.533333\pi$
$440$		0			0
$441$	−0.923665	+	2.84275i	−0.923665	+	2.84275i
$442$		0			0
$443$	1.73767	+	0.564602i	1.73767	+	0.564602i	0.994522	−	0.104528i	$-0.0333333\pi$
$443$	1.73767	+	0.564602i	1.73767	+	0.564602i	0.743145	+	0.669131i	$0.233333\pi$
$444$		0			0
$445$		0			0
$446$	3.30524	−	1.07394i	3.30524	−	1.07394i
$447$		0			0
$448$		0			0
$449$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$449$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$450$	5.46125			5.46125
$451$		0			0
$452$		0			0
$453$	1.27877	−	1.76007i	1.27877	−	1.76007i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$457$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.0646021	−	0.198825i	0.0646021	−	0.198825i	−0.913545	−	0.406737i	$-0.866667\pi$
$461$	0.0646021	−	0.198825i	0.0646021	−	0.198825i	0.978148	+	0.207912i	$0.0666667\pi$
$462$		0			0
$463$	0.809017	+	0.412215i	0.809017	+	0.412215i	0.809017	−	0.587785i	$-0.200000\pi$
$463$	0.809017	+	0.412215i	0.809017	+	0.412215i			1.00000i	$0.5\pi$
$464$	0.220124	−	0.0348642i	0.220124	−	0.0348642i
$465$		0			0
$466$	1.60244	−	3.14496i	1.60244	−	3.14496i
$467$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	−10.4455	+	5.32223i	−10.4455	+	5.32223i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.888244	−	1.22256i	−0.888244	−	1.22256i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.135231	+	0.135231i	0.135231	+	0.135231i
$479$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$479$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	2.22382	+	0.722562i	2.22382	+	0.722562i
$485$		0			0
$486$	1.68762	+	10.6552i	1.68762	+	10.6552i
$487$	−1.86055	+	0.604528i	−1.86055	+	0.604528i	−0.866025	+	0.500000i	$0.833333\pi$
$487$	−1.86055	+	0.604528i	−1.86055	+	0.604528i	−0.994522	+	0.104528i	$0.966667\pi$
$488$		0			0
$489$	−0.587257	+	0.587257i	−0.587257	+	0.587257i
$490$		0			0
$491$	−1.48629			−1.48629			−0.743145	−	0.669131i	$-0.766667\pi$
$491$	−1.48629			−1.48629			−0.743145	+	0.669131i	$0.766667\pi$
$492$	4.66371	+	0.244415i	4.66371	+	0.244415i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.977920	+	3.00973i	0.977920	+	3.00973i
$497$		0			0
$498$		0			0
$499$	−0.243145	+	1.53516i	−0.243145	+	1.53516i	0.500000	+	0.866025i	$0.333333\pi$
$499$	−0.243145	+	1.53516i	−0.243145	+	1.53516i	−0.743145	+	0.669131i	$0.766667\pi$
$500$		0			0
$501$			1.81347i			1.81347i
$502$		0			0
$503$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$503$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.64434	+	3.22720i	−1.64434	+	3.22720i
$508$	1.89169	−	1.37440i	1.89169	−	1.37440i
$509$	0.461219	−	0.235003i	0.461219	−	0.235003i	−0.207912	−	0.978148i	$-0.566667\pi$
$509$	0.461219	−	0.235003i	0.461219	−	0.235003i	0.669131	+	0.743145i	$0.266667\pi$
$510$		0			0
$511$		0			0
$512$	−1.25151	−	1.72256i	−1.25151	−	1.72256i
$513$		0			0
$514$	1.96571	+	0.311337i	1.96571	+	0.311337i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−2.28511	−	2.28511i	−2.28511	−	2.28511i
$520$		0			0
$521$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$521$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$522$	−0.259519	−	0.509335i	−0.259519	−	0.509335i
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		−	4.57433i		−	4.57433i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.309017	+	0.951057i	0.309017	+	0.951057i
$530$		0			0
$531$	−1.08583	+	1.49452i	−1.08583	+	1.49452i
$532$		0			0
$533$	1.40674	−	0.913545i	1.40674	−	0.913545i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.19231	+	3.66956i	1.19231	+	3.66956i
$538$	0.722562	−	0.234775i	0.722562	−	0.234775i
$539$		0			0
$540$		0			0
$541$	1.64728	+	0.535233i	1.64728	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$541$	1.64728	+	0.535233i	1.64728	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$542$			2.14787i			2.14787i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.770236	+	0.770236i	0.770236	+	0.770236i	0.978148	−	0.207912i	$-0.0666667\pi$
$547$	0.770236	+	0.770236i	0.770236	+	0.770236i	−0.207912	+	0.978148i	$0.566667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	4.82342	+	0.763955i	4.82342	+	0.763955i
$553$		0			0
$554$	−1.59618	−	2.19696i	−1.59618	−	2.19696i
$555$		0			0
$556$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$557$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$557$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$558$	6.56680	−	4.77106i	6.56680	−	4.77106i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$563$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$564$	1.81640	−	5.59031i	1.81640	−	5.59031i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.714192	+	4.50923i	0.714192	+	4.50923i
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$		0			0
$571$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$571$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.00000			−1.00000
$576$	0.898083	−	1.23611i	0.898083	−	1.23611i
$577$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−0.406737	+	0.913545i	$0.633333\pi$
$577$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−0.913545	+	0.406737i	$0.866667\pi$
$578$	0.564602	+	1.73767i	0.564602	+	1.73767i
$579$	−3.18612	+	1.03523i	−3.18612	+	1.03523i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.314190	+	0.966977i	−0.314190	+	0.966977i
$585$		0			0
$586$		0			0
$587$	−0.707912	+	0.112122i	−0.707912	+	0.112122i	−0.500000	−	0.866025i	$-0.666667\pi$
$587$	−0.707912	+	0.112122i	−0.707912	+	0.112122i	−0.207912	+	0.978148i	$0.566667\pi$
$588$	−3.30227	−	3.30227i	−3.30227	−	3.30227i
$589$		0			0
$590$		0			0
$591$	3.53964	−	1.80354i	3.53964	−	1.80354i
$592$		0			0
$593$	0.309017	+	0.0489435i	0.309017	+	0.0489435i	0.309017	−	0.951057i	$-0.400000\pi$
$593$	0.309017	+	0.0489435i	0.309017	+	0.0489435i			1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	2.73063	−	1.39132i	2.73063	−	1.39132i
$599$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$599$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$600$	−2.21708	+	4.35127i	−2.21708	+	4.35127i
$601$	−0.0740142	−	0.0740142i	−0.0740142	−	0.0740142i	0.669131	−	0.743145i	$-0.266667\pi$
$601$	−0.0740142	−	0.0740142i	−0.0740142	−	0.0740142i	−0.743145	+	0.669131i	$0.766667\pi$
$602$		0			0
$603$		0			0
$604$	1.15632	+	2.26941i	1.15632	+	2.26941i
$605$		0			0
$606$		−	3.31338i		−	3.31338i
$607$	−1.80902	−	0.587785i	−1.80902	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$607$	−1.80902	−	0.587785i	−1.80902	−	0.587785i	−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.652387	−	2.00784i	−0.652387	−	2.00784i
$612$		0			0
$613$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$613$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$614$	−2.14787			−2.14787
$615$		0			0
$616$		0			0
$617$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$617$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$618$		0			0
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$		0			0
$621$	−0.621457	−	3.92373i	−0.621457	−	3.92373i
$622$	−0.204857	+	1.29342i	−0.204857	+	1.29342i
$623$		0			0
$624$		−	7.13301i		−	7.13301i
$625$	0.309017	−	0.951057i	0.309017	−	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$	0.505539	+	0.367295i	0.505539	+	0.367295i
$634$	0.564602	+	0.0894242i	0.564602	+	0.0894242i
$635$		0			0
$636$		0			0
$637$	−1.65669	−	0.262394i	−1.65669	−	0.262394i
$638$		0			0
$639$	4.97273	−	2.53373i	4.97273	−	2.53373i
$640$		0			0
$641$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$641$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$642$		0			0
$643$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$643$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$647$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$648$	−11.5001	−	3.73662i	−11.5001	−	3.73662i
$649$		0			0
$650$	0.479418	+	3.02692i	0.479418	+	3.02692i
$651$		0			0
$652$	−0.300458	−	0.924716i	−0.300458	−	0.924716i
$653$	−0.506809	+	0.506809i	−0.506809	+	0.506809i	−0.913545	−	0.406737i	$-0.866667\pi$
$653$	−0.506809	+	0.506809i	−0.506809	+	0.506809i	0.406737	+	0.913545i	$0.366667\pi$
$654$		0			0
$655$		0			0
$656$	−1.06460	+	1.84395i	−1.06460	+	1.84395i
$657$	1.24291			1.24291
$658$		0			0
$659$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$659$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$660$		0			0
$661$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$661$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$662$	−0.444248	−	2.80487i	−0.444248	−	2.80487i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.0475201	+	0.0932634i	0.0475201	+	0.0932634i
$668$	−1.89169	−	0.963866i	−1.89169	−	0.963866i
$669$	3.75224	−	0.594296i	3.75224	−	0.594296i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.970554	−	0.494522i	0.970554	−	0.494522i	0.104528	−	0.994522i	$-0.466667\pi$
$673$	0.970554	−	0.494522i	0.970554	−	0.494522i	0.866025	+	0.500000i	$0.166667\pi$
$674$		0			0
$675$	3.92373	+	0.621457i	3.92373	+	0.621457i
$676$	−2.49243	−	3.43053i	−2.49243	−	3.43053i
$677$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$677$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.41228	−	1.41228i	−1.41228	−	1.41228i	−0.743145	−	0.669131i	$-0.766667\pi$
$683$	−1.41228	−	1.41228i	−1.41228	−	1.41228i	−0.669131	−	0.743145i	$-0.733333\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.221232	+	1.39680i	0.221232	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$691$	0.221232	+	1.39680i	0.221232	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$692$	3.59821	−	1.16913i	3.59821	−	1.16913i
$693$		0			0
$694$	−2.30227	+	2.30227i	−2.30227	+	2.30227i
$695$		0			0
$696$	0.511170			0.511170
$697$		0			0
$698$	3.57433			3.57433
$699$	2.26792	−	3.12152i	2.26792	−	3.12152i
$700$		0			0
$701$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$701$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$702$	−11.5789	+	3.76221i	−11.5789	+	3.76221i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		−	1.48629i		−	1.48629i
$707$		0			0
$708$	−1.31035	−	2.57170i	−1.31035	−	2.57170i
$709$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$709$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.20243	+	0.873619i	−1.20243	+	0.873619i
$714$		0			0
$715$		0			0
$716$	−4.46156	−	0.706642i	−4.46156	−	0.706642i
$717$	0.122881	+	0.169131i	0.122881	+	0.169131i
$718$		0			0
$719$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i		−	1.00000i	$-0.5\pi$
$719$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i	−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$723$		0			0
$724$		0			0
$725$	−0.103383	+	0.0163743i	−0.103383	+	0.0163743i
$726$	3.25144	+	1.65669i	3.25144	+	1.65669i
$727$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$727$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$728$		0			0
$729$			6.84745i			6.84745i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$		0			0
$735$		0			0
$736$	−0.849423	+	1.16913i	−0.849423	+	1.16913i
$737$		0			0
$738$	5.34191	+	1.13546i	5.34191	+	1.13546i
$739$	−1.33826			−1.33826			−0.669131	−	0.743145i	$-0.733333\pi$
$739$	−1.33826			−1.33826			−0.669131	+	0.743145i	$0.733333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$743$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$744$	1.13546	+	7.16900i	1.13546	+	7.16900i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$751$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$752$	1.89498	+	1.89498i	1.89498	+	1.89498i
$753$		0			0
$754$	0.259519	−	0.188552i	0.259519	−	0.188552i
$755$		0			0
$756$		0			0
$757$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$757$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.40126	−	1.01807i	−1.40126	−	1.01807i	−0.994522	−	0.104528i	$-0.966667\pi$
$761$	−1.40126	−	1.01807i	−1.40126	−	1.01807i	−0.406737	−	0.913545i	$-0.633333\pi$
$762$	3.25144	−	1.65669i	3.25144	−	1.65669i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.923665	−	0.470631i	−0.923665	−	0.470631i
$768$	−1.31035	−	2.57170i	−1.31035	−	2.57170i
$769$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$769$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$	2.06909	+	0.672288i	2.06909	+	0.672288i
$772$	0.613546	−	3.87377i	0.613546	−	3.87377i
$773$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$773$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$774$		0			0
$775$	−0.459289	−	1.41355i	−0.459289	−	1.41355i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.128496	−	0.395472i	−0.128496	−	0.395472i
$784$	2.02499	−	0.657960i	2.02499	−	0.657960i
$785$		0			0
$786$	1.11676	−	7.05097i	1.11676	−	7.05097i
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$			4.65090i			4.65090i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−1.60244	+	3.14496i	−1.60244	+	3.14496i
$795$		0			0
$796$		0			0
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$	−0.849423	−	1.16913i	−0.849423	−	1.16913i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	3.22085	+	3.22085i	3.22085	+	3.22085i
$807$	0.820282	−	0.129920i	0.820282	−	0.129920i
$808$	1.97815	+	1.00792i	1.97815	+	1.00792i
$809$	0.642040	+	1.26007i	0.642040	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$809$	0.642040	+	1.26007i	0.642040	+	1.26007i	−0.309017	+	0.951057i	$0.600000\pi$
$810$		0			0
$811$		−	1.98904i		−	1.98904i	−0.104528	−	0.994522i	$-0.533333\pi$
$811$		−	1.98904i		−	1.98904i	0.104528	−	0.994522i	$-0.466667\pi$
$812$		0			0
$813$	−0.367295	+	2.31901i	−0.367295	+	2.31901i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.07394	−	1.47815i	1.07394	−	1.47815i
$819$		0			0
$820$		0			0
$821$	−1.90211			−1.90211			−0.951057	−	0.309017i	$-0.900000\pi$
$821$	−1.90211			−1.90211			−0.951057	+	0.309017i	$0.900000\pi$
$822$		0			0
$823$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	−0.994522	−	0.104528i	$-0.966667\pi$
$823$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	0.104528	+	0.994522i	$0.466667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$827$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$828$	6.64709	+	2.15977i	6.64709	+	2.15977i
$829$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$829$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$830$		0			0
$831$	−1.34767	−	2.64496i	−1.34767	−	2.64496i
$832$	0.763955	+	0.389255i	0.763955	+	0.389255i
$833$		0			0
$834$	−2.09905	−	2.09905i	−2.09905	−	2.09905i
$835$		0			0
$836$		0			0
$837$	5.26094	−	2.68058i	5.26094	−	2.68058i
$838$		0			0
$839$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$839$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$840$		0			0
$841$	−0.581345	−	0.800153i	−0.581345	−	0.800153i
$842$		0			0
$843$		0			0
$844$	−0.651833	+	0.332126i	−0.651833	+	0.332126i
$845$		0			0
$846$	3.12062	−	6.12456i	3.12062	−	6.12456i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$			8.71985i			8.71985i
$853$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$853$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$857$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$858$		0			0
$859$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$859$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.244415	−	0.336408i	0.244415	−	0.336408i	−0.669131	−	0.743145i	$-0.733333\pi$
$863$	0.244415	−	0.336408i	0.244415	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$864$	4.05947	−	4.05947i	4.05947	−	4.05947i
$865$		0			0
$866$		0			0
$867$	0.312440	+	1.97267i	0.312440	+	1.97267i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.881623	+	1.73028i	−0.881623	+	1.73028i
$877$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$	−1.16681	+	0.594519i	−1.16681	+	0.594519i
$879$		0			0
$880$		0			0
$881$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$881$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$882$	−3.21005	−	4.41825i	−3.21005	−	4.41825i
$883$	−1.39680	−	0.221232i	−1.39680	−	0.221232i	−0.587785	−	0.809017i	$-0.700000\pi$
$883$	−1.39680	−	0.221232i	−1.39680	−	0.221232i	−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$		0			0
$886$	−2.70071	+	1.96218i	−2.70071	+	1.96218i
$887$	0.235003	−	0.461219i	0.235003	−	0.461219i	−0.743145	−	0.669131i	$-0.766667\pi$
$887$	0.235003	−	0.461219i	0.235003	−	0.461219i	0.978148	+	0.207912i	$0.0666667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−1.37440	+	4.22995i	−1.37440	+	4.22995i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	3.18612	−	1.03523i	3.18612	−	1.03523i
$898$		0			0
$899$	−0.110007	+	0.110007i	−0.110007	+	0.110007i
$900$	−4.10813	+	5.65435i	−4.10813	+	5.65435i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.22833	+	3.78042i	1.22833	+	3.78042i
$907$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$907$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$908$		0			0
$909$	0.424562	−	2.68058i	0.424562	−	2.68058i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$919$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$920$		0			0
$921$	−2.31901	−	0.367295i	−2.31901	−	0.367295i
$922$	0.224514	+	0.309017i	0.224514	+	0.309017i
$923$	1.84086	+	2.53373i	1.84086	+	2.53373i
$924$		0			0
$925$		0			0
$926$	−1.47815	+	0.753154i	−1.47815	+	0.753154i
$927$		0			0
$928$	−0.0686724	+	0.134777i	−0.0686724	+	0.134777i
$929$	0.889993	+	0.889993i	0.889993	+	0.889993i	0.994522	−	0.104528i	$-0.0333333\pi$
$929$	0.889993	+	0.889993i	0.889993	+	0.889993i	−0.104528	+	0.994522i	$0.533333\pi$
$930$		0			0
$931$		0			0
$932$	2.05075	+	4.02483i	2.05075	+	4.02483i
$933$	−0.442360	+	1.36144i	−0.442360	+	1.36144i
$934$		0			0
$935$		0			0
$936$	1.91773	−	12.1081i	1.91773	−	12.1081i
$937$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$937$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$944$	1.31592			1.31592
$945$		0			0
$946$		0			0
$947$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$947$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$	0.109110	+	0.688891i	0.109110	+	0.688891i
$950$		0			0
$951$	0.594296	+	0.193099i	0.594296	+	0.193099i
$952$		0			0
$953$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$953$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$954$		0			0
$955$		0			0
$956$	−0.241737	+	0.0382874i	−0.241737	+	0.0382874i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.978148	−	0.710666i	−0.978148	−	0.710666i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.461219	−	0.235003i	0.461219	−	0.235003i	−0.207912	−	0.978148i	$-0.566667\pi$
$967$	0.461219	−	0.235003i	0.461219	−	0.235003i	0.669131	+	0.743145i	$0.266667\pi$
$968$	−1.97815	+	1.43721i	−1.97815	+	1.43721i
$969$		0			0
$970$		0			0
$971$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$971$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$972$	−12.3014	−	6.26790i	−12.3014	−	6.26790i
$973$		0			0
$974$	1.10453	−	3.39939i	1.10453	−	3.39939i
$975$			3.35008i			3.35008i
$976$		0			0
$977$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$977$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$978$	−0.237376	−	1.49873i	−0.237376	−	1.49873i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.59618	−	2.19696i	1.59618	−	2.19696i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−3.07332	+	3.79523i	−3.07332	+	3.79523i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.278768	−	1.76007i	0.278768	−	1.76007i	−0.309017	−	0.951057i	$-0.600000\pi$
$991$	0.278768	−	1.76007i	0.278768	−	1.76007i	0.587785	−	0.809017i	$-0.300000\pi$
$992$	−2.04275	−	0.663730i	−2.04275	−	0.663730i
$993$		−	3.10432i		−	3.10432i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.95106	+	0.309017i	−1.95106	+	0.309017i	−0.951057	+	0.309017i	$0.900000\pi$
$997$	−1.95106	+	0.309017i	−1.95106	+	0.309017i	−1.00000			$1.00000\pi$
$998$	−2.00806	−	2.00806i	−2.00806	−	2.00806i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	943.1.n.b.689.1	yes	16
23.22	odd	2	CM	943.1.n.b.689.1	yes	16
41.5	even	20	inner	943.1.n.b.620.1	✓	16
943.620	odd	20	inner	943.1.n.b.620.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
943.1.n.b.620.1	✓	16	41.5	even	20	inner
943.1.n.b.620.1	✓	16	943.620	odd	20	inner
943.1.n.b.689.1	yes	16	1.1	even	1	trivial
943.1.n.b.689.1	yes	16	23.22	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 943 = 23 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	943.n (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07394 + 1.47815i) q^{2} +(-1.41228 + 1.41228i) q^{3} +(-0.722562 - 2.22382i) q^{4} +(-0.570857 - 3.60425i) q^{6} +(2.32545 + 0.755585i) q^{8} -2.98904i q^{9} +O(q^{10})\)	\(q+(-1.07394 + 1.47815i) q^{2} +(-1.41228 + 1.41228i) q^{3} +(-0.722562 - 2.22382i) q^{4} +(-0.570857 - 3.60425i) q^{6} +(2.32545 + 0.755585i) q^{8} -2.98904i q^{9} +(4.16110 + 2.12019i) q^{12} +(1.65669 - 0.262394i) q^{13} +(-1.72256 + 1.25151i) q^{16} +(4.41825 + 3.21005i) q^{18} +(-0.809017 - 0.587785i) q^{23} +(-4.35127 + 2.21708i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-1.39132 + 2.73063i) q^{26} +(2.80908 + 2.80908i) q^{27} +(-0.0932634 - 0.0475201i) q^{29} +(0.459289 - 1.41355i) q^{31} -1.44512i q^{32} +(-6.64709 + 2.15977i) q^{36} +(-1.96913 + 2.71028i) q^{39} +(0.913545 - 0.406737i) q^{41} +(1.73767 - 0.564602i) q^{46} +(-0.196895 - 1.24314i) q^{47} +(0.665249 - 4.20022i) q^{48} +(-0.951057 - 0.309017i) q^{49} +1.82709i q^{50} +(-1.78058 - 3.49458i) q^{52} +(-7.16900 + 1.13546i) q^{54} +(0.170401 - 0.0868235i) q^{58} +(-0.500000 - 0.363271i) q^{59} +(1.59618 + 2.19696i) q^{62} +(0.413545 + 0.300458i) q^{64} +(1.97267 - 0.312440i) q^{69} +(0.847673 + 1.66365i) q^{71} +(2.25848 - 6.95088i) q^{72} +0.415823i q^{73} +(-0.312440 + 1.97267i) q^{75} +(-1.89147 - 5.82133i) q^{78} -4.94534 q^{81} +(-0.379874 + 1.78716i) q^{82} +(0.198825 - 0.0646021i) q^{87} +(-0.722562 + 2.22382i) q^{92} +(1.34767 + 2.64496i) q^{93} +(2.04900 + 1.04402i) q^{94} +(2.04091 + 2.04091i) q^{96} +(1.47815 - 1.07394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6} + 2 q^{13} - 6 q^{16} + 6 q^{18} - 4 q^{23} - 22 q^{24} + 4 q^{25} + 12 q^{26} + 6 q^{27} - 8 q^{29} - 10 q^{36} + 2 q^{41} + 2 q^{47} - 18 q^{48} - 6 q^{54} + 2 q^{58} - 8 q^{59} - 10 q^{62} - 6 q^{64} - 2 q^{69} - 2 q^{71} + 16 q^{72} + 2 q^{75} - 2 q^{78} - 12 q^{81} + 10 q^{92} + 6 q^{93} + 18 q^{94} - 10 q^{96} + 6 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6 + 2 * q^13 - 6 * q^16 + 6 * q^18 - 4 * q^23 - 22 * q^24 + 4 * q^25 + 12 * q^26 + 6 * q^27 - 8 * q^29 - 10 * q^36 + 2 * q^41 + 2 * q^47 - 18 * q^48 - 6 * q^54 + 2 * q^58 - 8 * q^59 - 10 * q^62 - 6 * q^64 - 2 * q^69 - 2 * q^71 + 16 * q^72 + 2 * q^75 - 2 * q^78 - 12 * q^81 + 10 * q^92 + 6 * q^93 + 18 * q^94 - 10 * q^96 + 6 * q^98

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